On a q-Analog of ADHMN Construction for Self-Dual Yang-Mills

Abstract

It is known that many integrable systems can be reduced from self-dual Yang-Mills equations. The formal solution space to the self-dual Yang-Mills equations is given by the so called ADHM construction, in which the solution space are graded by vector spaces with dimensionality concerning topological index. When we consider a reduced self-dual system such as the Bogomol'nyi equations, in terms of ADHM construction, we need to incorporate an infinite dimensional vector space, in general. In this paper, we reformulate the ADHM construction by introducing various infinite dimensional vector spaces taking into account the reduction of self-dual system.